Question

The area of a circular play ground is 616m^2. A path of width 3 m is laid around and outside of it. Find the cost of levelling the path at rate of rupees 14/m^2

Answer 1

Given :

• Area of ground = 616 m²
• Width of path = 3 m
• Cost of levelling per m² = Rs 14

To Find :

• Cost of levelling the path

Solution :

$\Large \tt Area = \pi {r}^{2} \\ \\ \implies\tt616 = \frac{22}{7} \times {r}^{2} \\ \\\implies \tt {r}^{2} = 616 \times \frac{7}{22} \\ \\ \implies \tt {r}^{2} = 28 \times 7 \\ \\\implies \tt {r}^{2} =196 \\ \\ \implies\tt r = \sqrt{196} \\ \\\implies \tt r = 14 \: cm$

Ground + Circular path = New circle

Radius of new circle = 14 + 3 = 17 m

Area of new circle :

$\Large \tt Area = {\pi r}^{2} \\ \\\implies \tt area = \frac{22}{7} \times 17 \times 17 \\ \\ \implies\tt Area = \frac{6385}{7} \\ \\ \tt\implies Area = 912.14 \: {m}^{2}$

Area of path = Area of Ground - Area of new circle

$\implies\tt Area_{path} = 912.14 - 616 \\ \\\implies \tt Area_{path} =296.14 \: {m}^{2}$

Cost of levelling :

$\implies \tt cost \: of \: 1 \: {m}^{2} = 14 \\ \\ \implies\tt cost \: of \: 296.14 {m}^{2} = 14 \times 296.14 = 4146 \\ \\ \large \underline{\bf \green{ Cost\: of \:levelling\: the\: path = 4146 \:Rs}}$